The caustics of gravitational 'lenses'

When a galaxy acts as a gravitational "lens" it does not form a pointlike image of a pointlike source; instead, it forms caustic surfaces. This paper exploits the stationary-phase approximation for the Kirchhoff integral (adapted to curved space) to show that the intensity on the caustics of a spheroidal gravitational "lens" illuminated with waves from a point source is larger than the intensity of the undeflected waves. A large intensity gain occurs on and near the caustic in a neighborhood whose size is determined by diffraction effects.